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### On Perfect And Near-perfect Numbers - ScienceDirect

We call n a near-perfect number if n is the sum of all of its proper divisors, except for one of them, which we term the redundant divisor. For exampl… We call n a near-perfect number if n is the sum of all of its proper divisors, except for one of them, which we term the redundant divisor.
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### On The Density Of Spoof Odd Perfect Numbers

We study the set $\mathcal{S}$ of odd positive integers $n$ with the property
${2n}/{σ(n)} - 1 = 1/x$, for positive integer $x$, i.e., the set that
relates to odd perfect and odd "spoof perfect" numbers. As a consequence, we
find that if $D=pq$ denotes a spoof odd perfect number other than Descartes'
example, with pseudo-prime factor $p$, then $q>10^{12}$. Furthermore, we find
irregularities in the ending digits of integers $n\in\mathcal{S}$ and study
aspects of its density, leading us to conjecture that the amount of numbers in
$\mathcal{S}$ below $k$ is $\sim10 \log(k)$. Jan 24, 2021 ... As a consequence, we find that if D=pq denotes a spoof odd perfect number other than Descartes' example, with pseudo-prime factor p, ...
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### Can You Find A Perfect Number?

Can you find any perfect numbers? Read this article to find out more... Mathematicians noticed that some numbers are equal to the sum of all of their factors (but not including the number itself). 6 is a number that equals the sum ...
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### {\displaystyle {\begin{aligned}6=2^{1}\left(2^{2}-1\right)&=1+2+3 ...

### How To Write An Efficient Script For Perfect Numbers -

MathWorks is the leading developer of mathematical computing software for engineers and scientists. Discover… Explore Products.
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### What Are The Perfect Numbers And How To Use Them?

Jan 6, 2019 ... By now you know maths is not just a number system made up of whole numbers and clever counting. How about scientific notation, algebraic symbols ...
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### Spoof Odd Perfect Numbers

Oct 25, 2013 ... for such “spoof” odd perfect numbers, and construct an algorithm to find all such integers with a given number of distinct quasi-prime ...
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### Java - How To Find The 5th Perfect Number (which Is 33550336)? The ...

Dec 17, 2020 ... Let's check the properties of a perfect number. This Math Overflow question tells us two very interesting things: A perfect number is never ...
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### Euler's Odd Perfect Numbers Theorem | By Matthew Ward | Cantor's ...

An ancient proof to give insight into an unsolved problem. Jun 14, 2020 ... Most numbers are not perfect. In fact, you can quickly check for yourself that 6 is the smallest perfect number and then the next one is 28.
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### SIEVE METHODS FOR ODD PERFECT NUMBERS 1. Introduction A ...

Jan 9, 2012 ... Applying sieve techniques, we also find an upper bound on the smallest prime divisor. Putting this together we prove that an odd perfect number ...
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### Raji 4.4: 1. Find The Six Smallest Perfect Numbers. This Is The Same ...

Find the six smallest perfect numbers. This is the same as finding the six smallest Mersenne primes. So we must check Mp = 2p − 1 for primality for p = 2, ...
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